Topological photonics is a rapidly emerging field of research in which geometrical and topological ideas are exploited to design and control the behavior of light. Drawing inspiration from the discovery of the quantum Hall effects and topological insulators in condensed matter, recent advances have shown how to engineer analogous effects also for photons, leading to remarkable phenomena such as the robust unidirectional propagation of light, which hold great promise for applications. Thanks to the flexibility and diversity of photonics systems, this field is also opening up new opportunities to realize exotic topological models and to probe and exploit topological effects in new ways. This article reviews experimental and theoretical developments in topological photonics across a wide range of experimental platforms, including photonic crystals, waveguides, metamaterials, cavities, optomechanics, silicon photonics, and circuit QED. A discussion of how changing the dimensionality and symmetries of photonics systems has allowed for the realization of different topological phases is offered, and progress in understanding the interplay of topology with non-Hermitian effects, such as dissipation, is reviewed. As an exciting perspective, topological photonics can be combined with optical nonlinearities, leading toward new collective phenomena and novel strongly correlated states of light, such as an analog of the fractional quantum Hall effect.

Topological Photonics

Nearly a century after Einstein first predicted the existence of gravitational waves, a global network of Earth-based gravitational wave observatories1, 2, 3, 4 is seeking to directly detect this faint radiation using precision laser interferometry. Photon shot noise, due to the quantum nature of light, imposes a fundamental limit on the attometre-level sensitivity of the kilometre-scale Michelson interferometers deployed for this task. Here, we inject squeezed states to improve the performance of one of the detectors of the Laser Interferometer Gravitational-Wave Observatory (LIGO) beyond the quantum noise limit, most notably in the frequency region down to 150 Hz, critically important for several astrophysical sources, with no deterioration of performance observed at any frequency. With the injection of squeezed states, this LIGO detector demonstrated the best broadband sensitivity to gravitational waves ever achieved, with important implications for observing the gravitational-wave Universe with unprecedented sensitivity.

Enhanced sensitivity of the LIGO gravitational wave detector by using squeezed states of light

From Superfluid to Mott Insulator One of the most attractive characteristics of cold atomic gases in optical lattices is their ability to simulate condensed-matter systems. The results of these quantum simulations are usually averaged over the atomic ensemble, or course-grained over several lattice sites. Now, Bakr et al. (p. 547, published online 17 June; see the Perspective by DeMarco) provide a single lattice site view onto the transition of a Bose gas of Rb-87 from the superfluid to the Mott-insulating state. Characteristic concentric shells of uniform number density were observed deep in the Mott insulator regime, and probing the local quantum dynamics revealed unexpectedly short time scales. The low-defect Mott structures identified may provide a starting point for quantum magnetism experiments. Imaging of atoms that were optically trapped in lattice sites reveals local dynamics of a quantum phase transition. Quantum gases in optical lattices offer an opportunity to experimentally realize and explore condensed matter models in a clean, tunable system. We used single atom–single lattice site imaging to investigate the Bose-Hubbard model on a microscopic level. Our technique enables space- and time-resolved characterization of the number statistics across the superfluid–Mott insulator quantum phase transition. Site-resolved probing of fluctuations provides us with a sensitive local thermometer, allows us to identify microscopic heterostructures of low-entropy Mott domains, and enables us to measure local quantum dynamics, revealing surprisingly fast transition time scales. Our results may serve as a benchmark for theoretical studies of quantum dynamics, and may guide the engineering of low-entropy phases in a lattice.

Probing the Superfluid to Mott Insulator Transition at the Single Atom Level

We describe a simple technique for generating a cold-atom lattice pierced by a uniform magnetic field. Our method is to extend a one-dimensional optical lattice into the \"dimension\" provided by the internal atomic degrees of freedom, yielding a synthetic two-dimensional lattice. Suitable laser coupling between these internal states leads to a uniform magnetic flux within the two-dimensional lattice. We show that this setup reproduces the main features of magnetic lattice systems, such as the fractal Hofstadter-butterfly spectrum and the chiral edge states of the associated Chern insulating phases.

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Synthetic gauge fields in synthetic dimensions

radar echo delay, black holes and gravitational waves. It is worth pointing out that even here the author goes beyond a mere introduction, for example in the analysis of the phase diagram of cosmological parameters, the calculation of the first acoustic peak in the spectrum of the cosmic microwave background, the discussion of the precession of gyroscopes, the utilisation of Penrose diagrams to understand the causal structure of spacetime and the study of rotating black holes. Gravitational lensing, despite its important role in modern astronomy, is not covered at all. After just under 600 pages, the reader is already well versed in general relativity and many of its most important applications. Where many other textbook authors would have stopped, Zee goes on and continues with more advanced and modern subjects that will prepare the student to start doing research in the area. Maximally symmetric spaces, the vielbein formalism, conformal algebra, de Sitter and anti de Sitter spacetime, Kaluza– Klein theory, brane worlds, topological field theory and twistors are some of the more exotic topics the author addresses. These chapters make Zee’s book incredibly worthwhile, since treatments at the undergraduate level of these subjects hardly exist. All in all, Zee succeeded to write a unique textbook on general relativity. His narrative is exciting and well structured, but he also does not shy away from computations when they are necessary. The logical steps in attacking a problem are always presented very transparently, making it easier for the novice to become familiar with the material. The book is beautifully typeset and richly illustrated. It contains exercises at the end of each chapter and solutions to selected exercises in the appendix, together with a detailed index and a collection of important formulae. I strongly recommend this book to anyone interested in understanding general relativity.

Optical Magnetometry: Scope: reference. Level: postgraduate

We introduce a novel concept of the pseudo-parity-time (pseudo-PT) symmetry in periodically modulated optical systems with balanced gain and loss. We demonstrate that whether or not the original system is PT symmetric, we can manipulate the property of the PT symmetry by applying a periodic modulation in such a way that the effective system derived by the high-frequency Floquet method is PT symmetric. If the original system is non-PT symmetric, the PT symmetry in the effective system will lead to quasistationary propagation that can be associated with the pseudo-PT symmetry. Our results provide a promising approach for manipulating the PT symmetry of realistic systems.

https://openresearch-repository.anu.edu.au/bitstream/1885/74507/2/01_Luo_Pseudo-Parity-Time_Symmetry_in_2013.pdf

Pseudo-parity-time symmetry in optical systems.

Photonic waveguide arrays provide an excellent platform for simulating conventional topological systems, and they can also be employed for the study of novel topological phases in photonics systems. However, a direct measurement of bulk topological invariants remains a great challenge. Here we study topological features of generalized commensurate Aubry-Andre-Harper (AAH) photonic waveguide arrays and construct a topological phase diagram by calculating all bulk Chern numbers, and then explore the bulk-edge correspondence by analyzing the topological edge states and their winding numbers. In contrast to incommensurate AAH models, diagonal and off-diagonal commensurate AAH models are not topologically equivalent. In particular, there appear nontrivial topological phases with large Chern numbers and topological phase transitions. By implementing Thouless pumping of light in photonic waveguide arrays, we propose a simple scheme to measure the bulk Chern numbers.

Topological Phase Transitions and Thouless Pumping of Light in Photonic Waveguide Arrays

The study of topological effects in physics is a hot area of research, and only recently have researchers been able to address the important issues of topological properties of interacting quantum systems. But it is still a great challenge to describe multiparticle and interaction effects. Here, we introduce the multiparticle Wannier states for interacting systems with cotranslational symmetry, which provide an orthogonal basis for constructing effective Hamiltonians for the isolated bands. We reveal how the shift of multiparticle Wannier state relates to the Chern number of the multiparticle Bloch band and study the Thouless pumping of two interacting bosons in a one-dimensional superlattice. In addition to the Thouless pumping of bound states when two bosons move unidirectionally as a whole, we describe topologically resonant tunneling when two bosons move unidirectionally, one by the other, provided the neighboring-well potential bias matches the interaction energy. Our work creates a paradigm for multiparticle topological effects and provides a way to detect topological states in interacting multiparticle systems.

Multiparticle Wannier states and Thouless pumping of interacting bosons

We investigate continuous-time quantumwalks of two indistinguishable particles [two bosons, or two fermions, or two hard-core bosons (HCBs)] in one-dimensional lattices with nearest-neighbor interactions. The results for two HCBs are consistent with the recent experimental observation of two-magnon dynamics [Fukuhara et al., Nature (London) 502, 76 (2013)]. The two interacting particles can undergo independent walking and/or co-walking depending on both quantum statistics and interaction strength. Two strongly interacting particles may form a bound state and then co-walk like a single composite particle with a statistics-dependent walk speed. Analytical solutions for the scattering and bound states, which appear in the two-particle quantum walks, are obtained by solving the eigenvalue problem in the two-particle Hilbert space. In the context of degenerate perturbation theory, an effective single-particle model for the quantum co-walking is analytically derived and the walk speed of bosons is found to be exactly three times that of fermions and HCBs. Our result paves the way for experimentally exploring quantum statistics via two-particle quantum walks.

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Statistics-dependent quantum co-walking of two particles in one-dimensional lattices with nearest-neighbor interactions

Quantum metrology aims to yield higher measurement precisions via quantum techniques such as entanglement. It is of great importance for both fundamental sciences and practical technologies, from testing equivalence principle to designing high-precision atomic clocks. However, due to environment effects, highly entangled states become fragile and the achieved precisions may even be worse than the standard quantum limit (SQL). Here we present a high-precision measurement scheme via spin cat states (a kind of non-Gaussian entangled states in superposition of two quasi-orthogonal spin coherent states) under dissipation. In comparison to maximally entangled states, spin cat states with modest entanglement are more robust against losses and their achievable precisions may still beat the SQL. Even if the detector is imperfect, the achieved precisions of the parity measurement are higher than the ones of the population measurement. Our scheme provides a realizable way to achieve high-precision measurements via dissipative quantum systems of Bose atoms.

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Xizhou Qin

Papers

Pseudo-parity-time symmetry in optical systems.

Topological Phase Transitions and Thouless Pumping of Light in Photonic Waveguide Arrays

Multiparticle Wannier states and Thouless pumping of interacting bosons

Statistics-dependent quantum co-walking of two particles in one-dimensional lattices with nearest-neighbor interactions

Quantum metrology with spin cat states under dissipation.